The Convergence Problem in Mean Field Games with Neumann Boundary Conditions

In this article we study the convergence of the Nash Equilibria in a N-player differential game towards the optimal strategies in the Mean Field Games, when the dynamic of the generic player includes a reflection process which guarantees the invariance of the state space. The well-posedness of the Master Equation allows us to use its solution U in order to construct finite dimensional projections, which will converge, in some suitable spaces, to the solution of the Nash system.